Multidimensional Persistence is a method in topological data analysis
which allows to study several properties of a dataset contemporarily. It
is important to identify discrete invariants for multidimensional
persistence in order to compare properties of different datasets.
Furthermore such invariants should be stable, i.e., data sets which are
considered to be close should give close values of the invariant.

We introduce a framework that allows to compute a new class of stable
discrete invariants for multidimensional persistence. In doing this, we
generalize the notion of interleaving topology on multi-dimensional
persistence modules and consequently the notion of closeness for
datasets. A filter function is usually chosen to highlight properties we
want to examine from a dataset. Similarly, our new topology allows some
features of datasets to be considered as noise.